Finite Group DatabasebetaFinite Group Databasebeta| order | 1664 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C4 · Schur multiplier (H2) = C29 |
| direct product | C22×Q8×#261 |
| unambiguous semidirect product | D13⋊(C2×C4×Q8) |
| Fitting | C22×Q8×C13 ⋊ C4 |
| Sylow | C13 ⋊ C22×C4×Q8 |
1664 conjugacy classes of subgroups; only the 850 normal subgroups are shown.
This group has 1664 conjugacy classes of subgroups — too many to draw. Only its 850 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 416 |
140 conjugacy classes — view the full character table.
| maximal subgroup of | #16785420, #16785497, #261×#391, … |
| maximal normal subgroup of | #16785420, #16785497, #261×#391, … |
| maximal quotient of | C22×C4⋊C4×#261, C2×C4×Q8×#261, C22×#11719082, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1664, 21485);